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• BondsissuedincurrenciesotherthantheU.S.dollarconstitutemorethanhalfofthetaxablebondmarket,yetU.S.investorsgenerallyhavelittle,ifany,exposuretoforeignbondsintheirportfolios.

• Fortheaverageinvestorseekingtofurthermitigatevolatilityinadiversifiedportfolio,thispaperfindsthatforeignbondscanplay sucharole.

• Forinvestorslookingtoaddexposuretoforeignbonds,weshow thesubstantialbenefitsofhedgingtheimpactofforeignexchangemovements.

• Althoughnooneoptimalallocationfitsallportfolios,U.S.investorsconsideringinternationalbondsshouldbalancethediversificationbenefitsagainstboththecostsinvolvedandtheinherentbenefits ofpreservingacoreallocationtotheU.S.bondmarket.

Vanguard research February 2014

Globalfixedincome:ConsiderationsforU.S.investors

Authors

Christopher B. Philips, CFA

Joseph Davis, Ph.D.

Andrew J. Patterson, CFA

Charles J. Thomas, CFA

Note: This paper is an updated version of one originally published in 2006 by the same authors and titled International Equity: Considerations and Recommendations; the paper was also updated in 2009, 2011, and 2012.

2

1 While recognizing that usage varies widely, for the purposes of this paper we use the terms international and foreign to refer to bonds issued in currencies other than the U.S. dollar. However, because most of these bonds are investment-grade securities issued by developed countries, we focus on emerging-market bonds separately (see box on page 15).

2 The implications of such growth in government debt are widely debated, but are one reason investors may shy away from a globally market-weighted bond portfolio.

IMPORTANT: The projections or other information generated by the Vanguard Capital Markets Model® regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results, and are not guarantees of future results. VCMM results may vary with each use and over time. The VCMM projections are based on a statistical analysis of historical data. Future returns may behave differently from the historical patterns captured in the VCMM. More important, the VCMM may be underestimating extreme negative scenarios unobserved in the historical period on which the model estimation is based.

Notes on risk: All investments are subject to risk, including the possible loss of the money you invest. Past performance is no guarantee of future returns. Investments in bond funds are subject to interest rate, credit, and inflation risk. Investments in securities issued by non-U.S. companies are subject to risks including country/regional risk and currency risk. These risks are especially high in emerging markets. Currency hedging transactions incur extra expenses, may not perfectly offset foreign currency exposures, and may eliminate any chance to benefit from favorable fluctuations in those currencies. While U.S. Treasury or government agency securities provide substantial protection against credit risk, they do not protect investors against price changes due to changing interest rates. There is no guarantee that any particular asset allocation or mix of funds will meet your investment objectives or provide you with a given level of income. Diversification does not ensure a profit or protect against a loss. The performance of an index is not an exact representation of any particular investment, as you cannot invest directly in an index. ETF shares must be bought or sold in the secondary market with the assistance of a stockbroker. In doing so, the investor may incur brokerage commissions and may pay more than net asset value when buying and receive less than net asset value when selling.

Internationalbondscanbedefinedasdebt securitiesissuedbynon-U.S.governmentsandcorporations.1Althoughthesesecuritieshave alwaysrepresentedasignificantpartoftheglobalinvestablemarket,historicallytheyhaveentailed veryrealpracticalchallengesthatpreventedwidespreadusebyU.S.-basedinvestors(bothinstitutionalandindividual).Typicallythesemarketshavebeenilliquid,costly,andgenerallydifficult tonavigate.

However,thefirstdecadeofthe2000sbrought anaccelerationofglobalization,increasedaccess toinformation,ageneralliberalizationofworld creditmarkets,andwidespreadgrowthofdebt

issuanceabroad,primarilybygovernments.Thenetresult,intermsoftheglobalinvestablemarket(globalequitiesandfixedincome),hasbeenaneardoubling oftherelativeweightofthenon-U.S.bondmarketfromapproximately19%in2000toapproximately32%in2013(Figure 1).2And,inareflectionoftheeasingofinvestmentbarriers,investorstodayhaveaccesstovehiclessuchasbroadlydiversified,low-costexchange-tradedfunds(ETFs),whichmakeaddinganinternationalbondallocationtoaportfolioeasy.Theimplicationisclear:Investorscannowviewglobalbondsasanaccessibleandviableassetclasswiththepotentialtohelpreduceportfolioreturnvolatilityinamannersimilartothepotentialdiversificationbenefit ofinternationalequities.

3

3 Throughout this analysis we use the terms risk, volatility, and standard deviation of returns interchangeably.

Figure 1.

Global investable market components, 1995–2013

Non-U.S. bonds are now world’s largest asset class

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Notes: International bonds represented by Barclays Global Aggregate ex-USD Bond Index; U.S. bonds represented by Barclays U.S. Aggregate Bond Index; U.S. stocks represented by MSCI USA Index; international stocks represented by MSCI All Country World Index ex USA. All data through December 31, 2013.

Sources: Vanguard, Thomson Reuters Datastream, Barclays, and MSCI.

International stocksU.S. stocksInternational bondsU.S. bonds

2013201220112010200920082007200620052004200320022001200019991998199719961995

Aswithinternationalstocks,internationalbondsexposeinvestorstointerestratefluctuations,inflationandeconomiccycles,andissues associatedwithchangingorunstablepoliticalregimes.AlthoughtheseriskfactorsmayseemworrisometoU.S.investors,itisimportantto viewthemintheappropriatecontext.Forexample,whilethebondsofanyonecountrymaybemorevolatilethancomparablebondsintheUnitedStates, aninvestmentthatincludesthebondsofallcountriesandissuerscouldbenefitfromimperfectcorrelations

acrossthoseissuers.Infact,ouranalysisshows thatinaggregate,andwiththeappropriatehedging ofcurrencyrisk,aninvestmentinthebroadinternationalbondmarketcanbelessvolatilethan aninvestmentinthebroadU.S.bondmarket.3Forthisreason,investorsmightconsiderapproachingtheinternationalbondmarketsthroughabroadlydiversifiedindexfundorETFthatisweightedaccordingtomarketcapitalization(seethebox onpage4).

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Perhapsevenmoreimportant,exposuretointernationalriskfactorsmaybeworthwhileiftheoutlookfortheU.S.fixedincomemarketispoor. Inaddition,exposuretointernationalbondscouldofferclearlong-termdiversificationbenefitsifinternationalandU.S.marketfactorsaresufficientlydifferent,onaverage,overtime.Figure 2indicatesthatthisisthecase:Itshowsthedegreetowhichvariouscountries’levelsofinterestratesandinflation—thetwomostimportantdriversofbondreturns—havecorrelatedwiththeU.S.levelssince1990.TheselowandvariedcorrelationsareevidenceofthepotentialdiversificationbenefitofaddinginternationalbondstoaU.S.-onlybondportfolio.

The impact of adding international bonds to a diversified portfolio

Investingininternationalbondsentailsexposure tothemovementsofglobalcurrencies.Althoughcurrencymovementstendtobedrivenbyfundamentalfactorsoverlonghorizons,itiswelldocumentedthatcurrenciescananddodeviatesignificantlyfromfairvalueintheshorttointermediateterm.6Thesedeviationscreatereturnvolatilityabovethelevelinherenttotheunderlyinginvestment.Forexample,ifaU.S.investorwere topurchaseaGermanbunddenominatedin

4 For a discussion of the potential outcomes of the Eurozone sovereign debt crisis, see What’s Next for the Eurozone? (Lemco, Aliaga-Díaz, and Thomas, 2010).5 See Philips et al. (2011) for a discussion of alternative methodologies used to construct equity indexes and Thomas and Bennyhoff (2012) for a similar

analysis concerning fixed income benchmarks.6 Two theoretical models of currency value involve price level and interest rate differences between countries. Purchasing power parity (PPP) states that

identical goods sold in different countries must sell at the same price when translated into the same base currency. If PPP holds at the country level, real returns will be the same across countries, as exchange-rate movements and inflation differentials will offset each other. Interest rate parity (IRP) is based on the notion that the interest rate differential between the home and foreign markets will determine the change in the exchange rate, so that the realized rate of return on a risk-free government bond is the same in any market.

Doesn’t a market-cap-weighted index overweight the most indebted countries?

Theshortanswertothisquestionisyes,inthesensethatanymarket-cap-weightedbondindex willprovidegreaterexposuretoissuerswithmoredebtoutstanding.However,itisourviewthatmarketforcesaregenerallyefficientindemandingappropriatecompensationfortheexpectedriskofanyinvestment.Nogovernmentcansimplydumpitsdebtonthemarketwithoutanexpectationofanegativeimpact.Instead,themarketsetsapriceandyieldbasedontherisksoftheissuer.Acap-weightedindexapproachensuresthatinvestorsarematchingtherisk-and-returnprofileassignedbythebroadglobalbondmarket.

Thisissuehasreceivedmuchattentionsince theEuropeansovereign-debtcrisisbeganin 2010.Manyhavequestionedthewisdomof tyinginvestmentstoanindexwithexplicitexposuretoissuerssuchasGreece,acountryviewedashavingseriousdifficultiesinrepaying itsobligationsoverthenextfewyears.4Insuchcases,bondmarketparticipantsadjustprices

toreflecttheexpectedrisksandreturnofacountry’sdebt,includinganyprospectofa defaultorrestructuringevent.Thismeansthatinvestorsreceivealevelofyieldinlinewiththemarket’sassessmentoftherisksattendingagivencountry’sdebt,aswithanyotherbond.

Adeparturefrommarket-cap-weightedexposuretointernationalbondsassumesthatthemarket isincorrectinitsvaluationandthatthereisabetterwaytoinvest.Alternativestructures, suchasindexesweightedbyGDP,population, orlandmass,maysoundappealing,butlackanytheoreticalorrealeconomicrationaleasamethodforinvesting.Inaddition,thesemetricsconstitutefreelyavailableinformationandarethereforepricedintothecurrentvalueofagivenissue.Choosinganinvestmentstrategyotherthanacap-weightedindexmayinvolveasignificantdeparturefromthemarket’sexpectationofriskandreturn,andisthereforesomethingthatinvestorsmaywanttoconsidercarefullybeforeimplementing.5

5

euro,boththeinterestpaymentsandtheprincipalrepaymentwouldneedtobeconvertedfromeurointoU.S.dollars.Theconversionwouldtakeplace atthefutureexchangerate,whichcanchangeinwayseitheradverseorfavorabletothebondholder.IftheU.S.dollarweretoappreciate,theinvestorwouldreceivefewerdollarswhenthepaymentineurowasexchanged.Theoppositewouldbetrue ifthedollardepreciated.

Figure 3,onpage6,plotsthevolatility,definedhereastherolling36-monthstandarddeviationofreturns,inherenttotheU.S.dollarversusthreemajorcurrencies,aswellasthevolatilityinherenttothebroadU.S.stockmarketandthebroadinvestment-gradeU.S.bondmarket.(Note: We define investment-grade bonds as those fixed income securities rated

Baa3 and above by Moody’s Investors Service.) It’sclearthat,whilethevalueofthedollarhascycledbetweenperiodsoflowerandhighervolatility,onaverageitsvolatilityhasbeenbetweenthatofU.S.bondsandstocks.Becauseinternationalbondsentailexposuretocurrencyexchangerates,whichinthemselvesaremorevolatilethanthebroadU.S.bondmarket,thenaddinginternationalbondstoaportfoliowouldlikelyleadtoafixedincomeallocationwithgreatervolatilitythanistraditionallyassociatedwithU.S.bonds.Thekeyquestioniswhetherthe lowcorrelationofcurrencytotraditionalfinancialassetsoffersenoughbenefittoinvestorstoovercometheinherentvolatilityofcurrency.7

7 Portfolio variance is a function of the weight and variance of each asset in the portfolio, as well as the covariance of each asset with every other asset: ϴ2

portfolio = (w2d*ϴ

2d ) + (w2

f*ϴ2f ) + (w2

c*ϴ2c ) + (2*wd*wf*covdf ) + (2*wd*wc*covdc) + (2*wf*wc*covfc), where wd,f,c represents the weights of domestic bonds,

international bonds, and currency in the portfolio; ϴ2d,f,c represents their respective variances; and covdf,dc,fc represents the respective covariances among

the returns on the domestic bonds, international bonds, and the currency basket.

Figure 2.

Correlations of key drivers of bond returns in largest international markets versus United States, 1990–2013

In�ation and bond yields in international markets show low average correlation with U.S. levels

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Sources: Vanguard, U.S. Federal Reserve, U.S. Bureau of Labor Statistics, and various international government agencies via Thomson Reuters Datastream.

Change in long government bond yieldChange in in�ation

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In Figure 4weevaluatethehistoricalimpactofaddingbothunhedgedinternationalstocksandunhedgedinternationalbondstoa60%U.S. stock/40%U.S.bondportfolio.8Portfoliovolatility,definedastheannualizedstandarddeviationofmonthlyreturns,isminimizedinareaswiththedarkestgreenshading.ThecoloringofthefigureimpliesthataddinganyamountofunhedgedinternationalbondstoanycombinationofU.S.stocks,internationalstocks,andU.S.bondswouldhaveresultedinaportfoliomorevolatile,onaverage,

thanonewithoutinternationalbonds.9Infact,theleast-volatileportfolio,highlightedatthetopof thechart,hasnointernationalbondsatall—itis 42%U.S.stocks,18%internationalstocks,and 40%U.S.bonds.Givenanobjectiveofminimizingvolatility,Figure4alsoshowsthatasinvestorsincreasetheirallocationtounhedgedinternationalbonds,internationalstocksmaybereplaced,so thataninvestorallocating100%ofafixedincomeportfoliotointernationalbondsmightwanttoconsidera0%allocationtointernationalequities.10

8 For the purposes of this and other analyses in this paper, we define the returns of each asset class as follows: U.S. stocks are represented by the MSCI USA Index. U.S. bonds are represented by the Barclays U.S. Aggregate Bond Index. International stocks are represented by the MSCI World ex USA Index through 1987 and the MSCI All Country World Index ex USA through 2013. International bonds are represented by the Citigroup World Government Bond Ex-US Index through 1989 and the Barclays Global Aggregate ex-USD Bond Index through 2013.

9 Actively managed global bond portfolios may partially hedge their exchange-rate exposure as part of a currency overlay strategy. This paper considers only passively managed international bond portfolios.

10 Because investing in unhedged international bonds has a direct impact on the allocation to international equities, investors choosing to invest in international bonds should carefully consider the consequences to their entire portfolio. For more on the decision to invest in international equities, see Vanguard’s research paper Global Equities: Balancing Home Bias and Diversification (Philips, 2014).

Figure 3.

Relative to U.S. bond market, currencies have demonstrated greater volatility over time.

Volatility of three major currencies versus U.S. stock and bond markets, 1985–2013

Notes: Currency volatility represented by changes in the exchange rate of each currency shown relative to the U.S. dollar; U.S. bonds represented by Barclays U.S. Aggregate Bond Index; U.S. stocks represented by MSCI USA Index. For the period 1985 to 1999, before the creation of the euro, we used the exchange rate of the German deutsche mark to the U.S. dollar, as the German economy represents the primary driver of the euro’s value. The deutsche mark is very similar to a number of synthetic euro series designed to measure the currency’s value prior to its inception. For example, before 1999, the deutsche mark was highly correlated with the euro series from Moody’s Analytics, with a correlation of 1.00. All data through December 31, 2013.

Sources: Vanguard, Thomson Reuters Datastream, U.S. Federal Reserve, Barclays, Dow Jones, and MSCI.

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This chart shows how the average volatility changes for a 60% stock/40% bond portfolio when unhedged international securities are added by degrees, based on data for the period 1985–2013. Numbers in the chart represent the annualized standard deviation of monthly returns, with green indicating the lowest average volatility (i.e., the best outcome) and red the highest (i.e., the worst). The least-volatile portfolio, highlighted in the top row, contains no international bonds.

Currency exposure in bonds historically has increased volatility of balanced portfolios

Notes: U.S. stocks represented by MSCI USA Index; U.S. bonds represented by Barclays U.S. Aggregate Bond Index; international stocks represented by MSCI World ex USA Index through 1987 and MSCI All Country World Index ex USA thereafter; international bonds represented by Citigroup World Government Bond Ex-US Index through 1989 and Barclays Global Aggregate ex-USD Index thereafter.

Sources: Vanguard, Thomson Reuters Datastream, Barclays, Citigroup, Dow Jones, and MSCI.

Percentage in international stocks

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Ofparticularinterestisthecontrastbetween Figure2andFigure4.Intuitively,ifthecomponentsofinternationalbondreturnsareimperfectlycorrelatedwiththoseofU.S.bondreturns,it standstoreasonthatadiversificationbenefitshouldensue:Overallportfoliovolatilityshouldbereduced.However,Figure4reflectstherealitythatanysuchcorrelationbenefitisoverwhelmedbythesheermagnitudeofthecurrencyvolatilitiesshowninFigure3.11Inotherwords,thecurrencyexposureinherentininternationalbondsdominatestheirvolatility,negatinganydiversificationbenefitsthatmightbeexpectedotherwise.ThisresultsinanegativecorrelationbetweenunhedgedinternationalbondsandtheU.S.dollar,andfurtherdemonstratesthatanyallocationtounhedgedinternationalbondsrepresentsabearishviewabouttheperformance oftheU.S.dollar,whetherthatistheinvestor’sintendedobjectiveornot(seeFigure 5).

Althoughanallocationtounhedgedinternationalbondswouldbeexpectedtoincreaseaportfolio’saveragevolatilityovertime,theremaybecircum-stancesinwhichsuchanallocationwouldbedesirable.First,perceiveddiversificationbenefitsmaydependmoreonphysicalexposurethan onvolatility:Someinvestorsmayconsiderthe lattertobeamarginalconcerncomparedwiththeimplicationsofexcludingtheworld’ssinglelargestassetclassfromadiversifiedportfolio.Inaddition,someinvestorsmayhaveliabilitiesdenominated inforeigncurrencythattheywishtomorecloselymatchwiththeirassets.Forexample,aninstitutionmayhaveaforeign-domiciledpensionrequirementthatcouldbebettermanagedthroughtheuse ofunhedgedforeignbonds.12Finally,investors maynothavethedesireorcapabilitytomanagecurrencyrisk.Inanycase,theimplicationsof

Figure 5. An inverse relationship exists between U.S. dollar and unhedged international bond returns

Notes: International bonds represented by Citigroup World Government Bond Ex-US Index through 1989 and Barclays Global Aggregate ex-USD Index thereafter. The U.S. dollar is represented by the Federal Reserve’s Nominal Major Currencies Trade-Weighted Dollar Index. The correlation of monthly returns for unhedged international bonds to the U.S. dollar index is –0.6. All data through December 31, 2013.

Sources: Vanguard, Thomson Reuters Datastream, Barclays, Citigroup, and U.S. Federal Reserve.

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11 The return volatility of a global bond portfolio is a function of the volatility of the U.S. portion of the portfolio, the volatility of the local-currency international bond returns, the volatility of the international bonds’ currency basket, and the covariances among those components. See footnote 7 for the equation outlining the relationship.

12 Generally speaking, a U.S. pension following a liability-driven investment strategy would use long-duration U.S. bonds to minimize tracking error relative to its pension liability. International bonds are inappropriate for this investment objective unless the pension liability is computed using an international reference rate or contains a foreign currency component (or both). For additional discussion on investing using a liability-driven strategy, see Vanguard’s research paper Liability-Driven Investing: A Tool for Managing Pension Plan Funding Volatility (Stockton, Donaldson, and Shtekhman, 2008).

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includinginternationalbondsinaportfolio,with orwithouthedging,dependoneachinvestor’sspecificobjective.

The case for hedging currency risk

Wheninvestinginanyforeignasset,investors mustdecidewhethertoleavethecurrency exposureintactorattempttoremoveitthroughhedging.Choosingtohedgewilltietheinvestmentreturntotheperformanceoftheunderlyingassetalone(lessthecostsofhedging).Forexample,Figure 6showsthatwhentheeffectofcurrencyexposureisremoved,internationalbondsassume areturnprofilethatismuchmore“bond-like.”

Figure 7,onpage10,showsthehistoricalimpact ofincludingahedgedinternationalbondallocation inabalancedportfolio.AsinFigure4,portfoliovolatilityisminimizedattheareawiththedarkest-

greenshading.Itisinterestingthat,oncethecurrencyriskisremovedthroughhedging,the least-volatileportfoliois42%U.S.stocks,18%internationalstocks,and40%internationalbonds.Further,withbondcurrencyrisknegated,theinclusionofinternationalbondshasrelatively littleeffectontheallocationdecisionregardinginternationalstocks.Inotherwords,a30%allocationtointernationalstockswithintheequityportionoftheportfolio(18%dividedby60%)remainsoptimalforreducingvolatilityovertheperiodanalyzed,regardlessofthelevelofinternationalbondallocation.Thismakesiteasierforinvestorstoassesstheimpactofaddinginternationalbondstoaportfolio. Inaddition,wefindthathedgedinternationalbondshistoricallyhaveofferedconsistentrisk-reductionbenefits:Portfoliovolatilitydecreaseswitheachincrementalallocationtointernationalbonds.

Figure 6. With currency exposure hedged, international bonds show more bond-like characteristics

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Notes: International bonds represented by Citigroup World Government Bond Ex-US Hedged Index through 1989 and Barclays Global Aggregate ex-USD Hedged Index thereafter; U.S. bonds represented by Barclays U.S. Aggregate Bond Index. The correlation of monthly returns for hedged international bonds to U.S. bonds is 0.6. All data through December 31, 2013.

Sources: Vanguard, Thomson Reuters Datastream, Barclays, Citigroup, and U.S. Federal Reserve.

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This chart shows how the average volatility changes for a 60% stock/40% bond portfolio with the addition of hedged international bonds and unhedged international stocks. Like Figure 4, it is based on data for the period 1985–2013; the numbers represent the annualized standard deviation of monthly returns, with green indicating the lowest volatility and red the highest. Unlike Figure 4, in this chart the least-volatile portfolio (highlighted) holds only international bonds for its �xed income portion.

Adding hedged international bonds historically has decreased the volatility of balanced portfolios

Notes: U.S. stocks represented by MSCI USA Index; U.S. bonds represented by Barclays U.S. Aggregate Bond Index; international stocks represented by MSCI World ex USA Index through 1987 and MSCI All Country World Index ex USA thereafter; international bonds represented by Citigroup World Government Bond Index Ex-US Hedged Index through 1989 and Barclays Global Aggregate ex-USD Hedged Index thereafter. All data through December 31, 2013.

Sources: Vanguard, Thomson Reuters Datastream, Barclays, Citigroup, Dow Jones, and MSCI.

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9.6 9.5 9.5 9.4 9.4 9.4 9.4 9.4 9.4 9.5 9.5 9.6 9.7 9.8 10.0 10.1 10.3 10.4 10.6 10.8 11.0

9.6 9.5 9.4 9.4 9.4 9.3 9.4 9.4 9.4 9.5 9.5 9.6 9.7 9.8 10.0 10.1 10.3 10.4 10.6 10.8 11.0

9.6 9.5 9.4 9.4 9.3 9.3 9.3 9.4 9.4 9.4 9.5 9.6 9.7 9.8 9.9 10.1 10.2 10.4 10.6 10.8 11.0

9.5 9.5 9.4 9.4 9.3 9.3 9.3 9.3 9.4 9.4 9.5 9.6 9.7 9.8 9.9 10.1 10.2 10.4 10.6 10.8 11.0

9.5 9.5 9.4 9.3 9.3 9.3 9.3 9.3 9.4 9.4 9.5 9.6 9.7 9.8 9.9 10.1 10.2 10.4 10.6 10.8 11.0

9.5 9.4 9.4 9.3 9.3 9.3 9.3 9.3 9.4 9.4 9.5 9.6 9.7 9.8 9.9 10.1 10.2 10.4 10.6 10.8 11.0

9.5 9.4 9.4 9.3 9.3 9.3 9.3 9.3 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10.0 10.2 10.4 10.5 10.7 10.9

9.5 9.4 9.4 9.3 9.3 9.3 9.3 9.3 9.3 9.4 9.5 9.5 9.6 9.8 9.9 10.0 10.2 10.4 10.5 10.7 10.9

9.5 9.4 9.3 9.3 9.3 9.3 9.3 9.3 9.3 9.4 9.4 9.5 9.6 9.7 9.9 10.0 10.2 10.4 10.5 10.7 10.9

9.5 9.4 9.3 9.3 9.3 9.2 9.2 9.3 9.3 9.4 9.4 9.5 9.6 9.7 9.9 10.0 10.2 10.3 10.5 10.7 10.9

9.5 9.4 9.3 9.3 9.2 9.2 9.2 9.3 9.3 9.4 9.4 9.5 9.6 9.7 9.9 10.0 10.2 10.3 10.5 10.7 10.9

9.4 9.4 9.3 9.3 9.2 9.2 9.2 9.3 9.3 9.3 9.4 9.5 9.6 9.7 9.9 10.0 10.2 10.3 10.5 10.7 10.9

9.4 9.4 9.3 9.3 9.2 9.2 9.2 9.2 9.3 9.3 9.4 9.5 9.6 9.7 9.9 10.0 10.2 10.3 10.5 10.7 10.9

9.4 9.3 9.3 9.2 9.2 9.2 9.2 9.2 9.3 9.3 9.4 9.5 9.6 9.7 9.8 10.0 10.1 10.3 10.5 10.7 10.9

9.4 9.3 9.3 9.2 9.2 9.2 9.2 9.2 9.3 9.3 9.4 9.5 9.6 9.7 9.8 10.0 10.1 10.3 10.5 10.7 10.9

9.4 9.3 9.3 9.2 9.2 9.2 9.2 9.2 9.3 9.3 9.4 9.5 9.6 9.7 9.8 10.0 10.1 10.3 10.5 10.7 10.9

9.4 9.3 9.3 9.2 9.2 9.2 9.2 9.2 9.3 9.3 9.4 9.5 9.6 9.7 9.8 10.0 10.1 10.3 10.5 10.7 10.9

11

A framework for asset allocation

Figure7showsthat,onthebasisofhistorical data,avolatility-minimizinginvestorwouldhave beenbetteroffoverthelast28yearswitha sizableallocationtohedgedinternationalbonds. Itis,however,importanttoconsidertheeconomicandfinancialenvironmentinthequarter-century thatproducedtheseresults.Duringthisperiod, theUnitedStatesandotherdevelopedmarketsexperiencedfallinginterestrates,disinflation,andtheanchoringoflong-terminflationexpectations.Togetherthesetrendscreatedafavorablereturnenvironmentforbondinvestors(returnsaveraged7.5%annuallyfordiversifiedU.S.bonds,8.6%annuallyforunhedgedinternationalbonds,and6.7%annuallyforhedgedinternationalbonds).Giventheenvironmenttoday,bondinvestorsmustask:

1. Arereturnexpectationsbasedonhistoryreasonable?

2. Shouldhedgingcurrencyriskbeexpectedtoleadtolowerreturns?

3.Doassetallocationconclusionschangeasreturnexpectationschange?

Toaddressthefirstquestion,itisimportanttonotethatinterestratestodayaremuchlowerthantheywerein1985.Absenthighyieldsatthestart,thehistoricalreturnscenarioisnotlikelytoberepeated.Inaddition,currentinflationexpectations,arguablythemostimportantdriverofinterestratelevels, arelargelystableacrossdevelopedmarkets.Thissuggeststhatascenarioinwhichinterestratesclimbsignificantlytothelevelsseeninthe1980s—thoughpossible—maybeviewedashavingalowprobability.Giventhemarketandeconomic

conditionsin2013,alikelyforward-lookingscenarioisoneinwhichnominalyieldsacrossdevelopedmarketsrisegradually,creatingadragonbondreturnsintheshortterm,butcompensatinginvestorswithhigheryieldsovertime.13Asaresult,investorsmaywanttostartwithcurrentlevelsofyieldasthebaselineforforwardlong-termreturnexpectationsandthenpossiblyfactorinamodestpremiumtoaccountforanincreaseinincomeasyieldsrisetomorenormallevels.

The28yearsthrough2013alsowerecharacterizedbylong-termdepreciationoftheU.S.dollar.Thisis whyunhedgedinternationalbondsoutperformedhedgedbondsby1.9percentagepointsayear,onaverage.SinceunhedgedbondsheightenportfoliovolatilityandsuggestabearishviewontheU.S.dollar,thecriticalquestionsthenare:ShouldinvestorsexpecttheU.S.dollartocontinuealong-termslide,andwouldsuchdepreciationeffectivelycounterthehighervolatility?Investorsconsideringthesepointsshouldnotethatshort-termcurrencymovementsarewidelythoughttofollowarandomwalk(Solnik,1974;MeeseandRogoff,1983;PeroldandSchulman,1988).Althoughthereisevidencethatoveralong-enoughtimehorizon,structuraldifferencesbetweencountriescanforcecurrenciestoafundamentalequilibrium(MeredithandChinn,1998;Mark,1995),thesestructuralfactors—pricelevelsandtradeflows,forexample—areinherentlylong-terminnature,andchangesinthemthereforetendtobeanticipatedandpricedinbysecuritiesmarkets.Asaresult,webelievethatanallocationtounhedgedinternationalbondsthatisdrivenbyviewsonpotentialcurrencyreturnsshouldbeconsideredwithcare.

13 For more on Vanguard’s outlook for the U.S. fixed income market, see Vanguard’s Economic and Investment Outlook (Davis et al., 2014).

12

14 For more on the decision of whether to hedge currency in an international stock portfolio, see Vanguard’s research paper Currency Management: Considerations for the Equity Hedging Decision (LaBarge, 2010).

Why hedge international bonds and not international stocks?

Anaturalquestionarisingfromthisreportis whethercurrencyriskshouldalsobehedged withinaninternationalequityallocation.Whenconsideringthisquestion,it’sessentialtorecalltherelationshipbetweenassetvolatilityandcurrencyvolatility.Asexplainedinfootnote7 (page5),thecorrelationsoftheassetscombinewiththevolatilitiesoftheassetstoresultinatotalvolatilitystatistic.Inthecaseofbonds,currencyexposureaddssignificantvolatilitytoanassetthat

isrelativelystableinprice.Stocks,ontheotherhand,alreadyhavehighvolatility,sotheeffect ofaddingcurrencyvolatilityislesspronounced.TheserelationshipsareshowninFigure 8.Forinternationalstocks,thebenefitofhedgingissmaller,whilethecostsremainthesame.14 On theotherhand,thebenefitsofhedgingcurrencyriskininternationalbondportfoliosgenerallyoutweighthecosts.

Figure 8.

Mitigating currency volatility would have had a modest effect on the overall volatility of stocks, but a meaningful effect on the volatility of bonds. This chart re�ects annualized returns and volatility for the period 1985–2013.

Hedging currency risk has much greater impact on bonds than on stocks

Notes: International stocks represented by MSCI World ex USA Index through 1987 and MSCI All Country World Index ex USA thereafter; international bonds represented by Citigroup World Government Bond Ex-US Hedged Index through 1989 and Barclays Global Aggregate ex-USD Hedged Index thereafter. All data through December 31, 2013.

Sources: Vanguard, Thomson Reuters Datastream, Barclays, Citigroup, Dow Jones, and MSCI.

Market contributionCurrency contribution

0

5

10

15

20

25%International stocks International bonds

Return Volatility VolatilityReturn

Ann

ual r

etur

n an

d vo

latil

ity

13

Finally,weturntothequestionofhowreturnexpectationsmightaffectourpreviousvolatility-focusedanalysis.Forthispurposeitisusefultoconstructanefficientfrontier,agraphshowingtheentiresetofassetcombinationsthatwouldachieveagivenexpectedreturnwiththeleastexpected riskunderspecifiedassumptions.

Asriskinputstothisanalysis,wetookthehistoricalvolatilitiesandcorrelationsbetweenglobalstocks,unhedgedglobalbonds,andhedgedglobalbonds(basedonthedataandtimeperiodlistedintheappendix).15Usingtheseinputs,wegeneratedthefullrangeofefficientportfoliosandthenevaluatedwhatamountofforeigncurrencyappreciation,beyondthe“expected”movementthatmightbecapturedintheforwardpremiumthroughhedging,wasneededforunhedgedbondstobecomeaviableinvestment.Webeganwiththeassumptionthatbothhedgedandunhedgedglobalbondsgeneratethesamelong-runreturn(inotherwords,unexpectedcurrencyreturnis0%andcurrencyreturnequalstheforwardpremiumoverthelongrun).Wethentestedtheviabilityofunhedgedbondsbysuccessivelyaddinganassumed“unexpected”currencyreturnandexaminingwhetherunhedgedbondsappearedonthefrontierinanymeaningfulallocation.

Figure 9,onpage14,displaystheresultsfortheparticularrangeofassumedforeigncurrencyappreciationinwhichunhedgedbondsbegintoappearasaviableinvestment.Wefoundthat,

untiloneassumesgreaterthan1.75%averageannualunexpectedcurrencyreturn(thatis,morethan1.75%averageannualforeigncurrencyappreciationbeyondthatrealizedthroughhedging),unhedgedbondsdonotappeartobeanassetclasswithexpectationsformeaningfulreturnandriskimpacttoagloballydiversifiedportfolio.Forfixed-income-orientedinvestors,hedgedbondsremainedthemoreviableoptionunderallofthecurrencyscenariosweexamined,withunhedgedbondsappearingonlyinmodestallocationsunderanyassumedunexpectedcurrencyreturn.Ittakesveryaggressiveassumptionsregardingunexpecteddollardepreciationforunhedgedbondstobecomeaviablelong-terminvestmentunderourframework,andeventhenonlyformoreequity-orientedinvestors.

Afollow-upquestionis:Howreasonableisittoexpectanyadditionalyearlyreturnfromexposure toabasketofcurrenciesoverthelongterm,relativetoahedgedinvestment?NotethatthisadditionalreturnwouldhavetoresultfromunexpectedfuturedislocationsbetweentheU.S.andglobaleconomies.Thatisbecausesecuritiesmarketsareforward-looking.Inotherwords,ifinvestorscollectivelybelievedcurrencieswouldheadinacertaindirection,theanticipatedcurrencyreturnwouldbefactoredintointermediate-andlong-maturitybondpricestoday.Thatsaid,giventheelevatedlevelsofuncertaintyintheglobaleconomicenvironment,unexpectedfuturedevelopmentscouldresultinsizablecurrencymovement.

15 The projections discussed here represent outcomes generated by the Vanguard Capital Markets Model for U.S. stocks, U.S. bonds, and international stocks. For both hedged and unhedged international bonds, we assumed that starting yields represented the best approximation for future returns. However, to account for the likelihood of rising interest rates, we added a 100-basis-point premium to expected bond returns. We assumed that historical volatilities and correlations were reasonable expectations going forward. For more information about the Vanguard Capital Markets Model, see the appendix.

14

Investorswishingtopositiontheirportfoliosforthepossibilityofsuchextreme,unexpecteddollardepre-ciationmayconsiderusingunhedgedinternationalbonds.Forexample,althoughbothU.S.stocksandU.S.bondshistoricallyhaveperformedwellduring

periodsofsignificantdollardepreciation,thereis noclearandconsistentrelationship,asonefindsbetweenunhedgedinternationalbondsandthedollarduringsuchperiods.16

16 Since 1985, dollar returns have explained less than 6% of the variance in both U.S. stocks and bonds (measured as the R-squared between security returns and those of the Federal Reserve’s trade-weighted dollar index), while the movement of the dollar explained 80% of unhedged international bonds’ returns, making them a much better hedge against adverse dollar scenarios. Over the same period, U.S. stocks and bonds returned 1.4% and 0.9%, respectively, on average during months in which the dollar declined by more than 1%. Unhedged international bonds returned 3.5% during those same months. Note: R-squared refers to a measure of how much of a security’s past returns can be explained by the returns from a given index.

Figure 9. Signi�cant long-term unexpected dollar depreciation is needed to make unhedged bonds a viable strategic investment

Notes: Figure displays proportion of the global bond allocation that is allocated to unhedged bonds versus hedged bonds under several assumptions on long-term foreign currency return, based on results of a portfolio optimization using inputs described on page 13 of this paper. U.S. stocks represented by MSCI USA Index; U.S. bonds represented by Barclays U.S. Aggregate Bond Index; international stocks represented by MSCI World ex USA Index through 1987 and MSCI All Country World Index ex USA thereafter; international bonds represented by Citigroup World Government Bond Index Ex-US Hedged Index through 1989 and Barclays Global Aggregate ex-USD Hedged Index thereafter. All data through December 31, 2013.

Sources: Vanguard and Thomson Reuters Datastream.

Per

cent

age

of �

xed

inco

me

allo

catio

nin

unh

edge

d fo

reig

n bo

nds

0

20

40

60

80

100%

0% 0% 0%5%

13%

34%

15%

39%

96%

26%

67%

100%

38%

95%100%

1.25% currency return 1.50% currency return 1.75% currency return 2.00% currency return 2.25% currency return

Hypothetical future unexpected currency depreciation

30% stocks/70% bonds50% stocks/50% bonds70% stocks/30% bonds

15

Emerging-market bonds

Likeemerging-marketstocks,fixedincomesecuritiesissuedbygovernmentsandcompaniesinemergingmarketsmayhavearoleinadiversifiedportfolio.However,totheextentthatemerging-marketbondsareratedinvestmentgrade,theymaybefoundintraditionalbroadindexes.Forexample,asofDecember31,2013,2%oftheBarclaysU.S.AggregateBondIndexwasallocatedtoemerging-marketbonds.Similarly,4%oftheBarclaysGlobalex-USDAggregateBondIndexconstitutedemerging-marketbonds.

Emerging-marketbondsaretypicallyofferedintwovariations,denominatedinamajorcurrencysuchasU.S.dollars,euro,orpoundssterling,ordenominatedinacountry’slocalcurrency.Traditionally,bondsdenominatedinU.S.dollarsweremorecommon;however,inrecentyearsbondsissuedinothermajorcurrenciesandlocalcurrencieshaveincreasedtheirmarketshare.Infact,todaylocal-currencyissuesaremorecommon(intermsofmarketcapitalization)thanissuesdenominatedinmajorcurrencies.

Emerging-marketbondsgenerallycarryhigheryieldsthandeveloped-marketbondsbecausetheycarrygreaterrisks,suchaspoliticalinstabilityoruncertaintyaboutinflation.Forthesamereason,emerging-marketbondshavealsoexperiencedsignificantlyhighervolatilitythandeveloped-marketbonds.However,becausethetwotypes ofmarketstendtohavequitedifferentrisks, wewouldexpectcorrelationsbetweentheirsecuritiestoberelativelylow,implyingapotentialdiversificationbenefit.Figure 10presentsthehistoricalcorrelationsbetweentraditionalfinancialassetsandbothU.S.dollar-denominatedandlocal-currency-denominatedemerging-marketbonds.Becauseofthesebonds’placeintheglobalmarket,aswellasthepotentialforadditionaldiversification,allocatingsomeassetstoemerging-marketbondsaspartofabroadlydiversifiedinternationalbondinvestmentcan makesenseforcertaininvestors.Formore ontheroleofemerging-marketbondsinadiversifiedportfolio,seePhilipsetal.(2013).

Figure 10.

Emerging-market bonds, regardless of their country or currency of issue, showed attractively low correlations with major asset classes, both hedged and unhedged, over the period 2002–2013.

Emerging-market bonds can provide additional diversi�cation bene�t

Notes: U.S. stocks represented by MSCI USA Index; U.S. bonds represented by Barclays U.S. Aggregate Bond Index; developed international stocks represented by MSCI World ex USA Index; international bonds represented by Barclays Global Aggregate ex-USD Index (Unhedged and Hedged); emerging-market stocks represented by MSCI Emerging Markets Index; emerging-market bonds represented by J.P. Morgan Emerging Markets Bond Index and J.P. Morgan Global Bond Index—Emerging Markets. All data through December 31, 2013.

Sources: Vanguard, Thomson Reuters Datastream, JPMorgan Chase, Barclays, Dow Jones, and MSCI.

Emerging-market bonds—U.S. dollar issuesEmerging-market bonds—Local issues in U.S. dollar termsEmerging-market bonds—Local issues in local-currency terms

0

0.2

0.4

0.6

0.8

U.S. stocks U.S. bonds Developedinternational

stocks

Internationalbonds

unhedged

Internationalbonds

hedged

Emergingmarketstocks

Cor

rela

tion

16

Impact of the forward premium

Investorsmayalsoconsideraccountingfor thecostofhedgingacurrencythatistrading ataforwardpremium(ordiscount)toitsspotexchangerate,aresultofa“noarbitrage”relationshipinshort-terminterestratediffer-entialsbetweentwocountries.Thiseffectcanbethoughtofasa“haircut”(ora“premium”)totheyield.Considerthisexample:AU.S.investorwantstopurchasea1-yearGermanbundandhedgehisexposuretotheeuro.Theinvestorwouldconverthisdollarstoeuroatthespotrateandpurchasethebund.Tohedgehis euroexposure,theinvestorwouldenterintoa1-yearforwardcontract,to“lockin”aforwardexchangerate.Often,theforwardcontractwillnotbeequaltothespotrate,resultinginaforwardpremiumordiscount.Alossontheforwardcontractcouldbeconsideredahaircuttothebond’syield,whileagainmaybeconsideredaboost.Ofcourse,thedollarmayalsobetradingataforwarddiscountrelativetoothercurrencies,thusreducingthepotentialforalargehaircutduetohedgingwheninvestingacrossseveralinternationalmarkets.

Generallyspeaking,hedgingisimplementedoverashorterhorizonthanintheaboveexample(typicallyoveraone-tothree-monthhorizon).Theshort-termratesusedtosetforwardexchangeratesatthesehorizons reflectacountry’scurrentmonetarypolicy,whileintermediate-andlong-termratesreflecteconomicfundamentalssuchasinflationdiffer-entials.Becauselong-termcurrencytrendsaredrivenbythefundamentalsreflectedinlongrates,anyforwardpremiumordiscountduetoshort-terminterestratedifferentialsbetweencountriesmaybeexpectedtowashoutovertime.ThisisespeciallytruewhencomparingtheUnitedStatestoamultilateralgroupofcountriesthatarelikelytobeindifferentstagesoftheirbusinesscycles.

Practical considerations for a long-term strategic investor

Beyondempiricalanalysis,additionalqualitativefactorssuchasportfolioobjectives,costs,and otheroperationalconsiderationscouldinfluence thedecisiontoincludeinternationalbondsinadiversifiedportfolio.Forexample:

• HoldingnoU.S.bonds(asobservedinFigure7)wouldrepresentasignificantdeviationnotonlyfromthecapitalizationweightingsintheglobalbondmarketbutalsofromthestandardassetallocationframeworkforU.S.investors.

• IgnoringtheU.S.fixedincomemarketinfavor ofbondsissuedabroadleavesnoexposuretoU.S.Treasurysecurities,aprovendiversifierduringeconomicandfinancialdownturns.

• Correlationsacrossdevelopedmarketshavedisplayedapersistentrisingtrendinbothequityandfixedincomemarkets.Ifthistrendcontinues,thediversificationbenefitsofinternationalsecuritieswilllikelydecreaseinmagnitude(thoughnotdisappear).

• Internationalbondsaregenerallygovernmentbonds.Forinvestorsseekinghigheryields,U.S.corporatebondsmaybeabetterfit.

• Foreignfixedincomemarketsarestillnotaseasilyaccessedasforeignequitymarkets,asdemonstratedbygenerallyhighertransactioncosts.

The costs of hedgingAnimportantconsiderationforaninvestor weighingthebenefitsofinternationalbondsisthepotentialcostofimplementingacurrencyhedge. Toexaminethisissue,Figure 11showsthehistoricalannualizedbid-askspreadon1-monthcurrencyforwardcontracts,areasonableapproximationof theannualtradingcostsofhedging.Notwithstandingthespikein2008–2009astheglobalrecessiontookhold,spreadshavetrendeddownwardandremain atlowlevels,suggestingthatinvestorsmightexpectminimaldragontheirreturnsrelativetothediversi-ficationbenefitsthatcanbeachieved.

17

Conclusion

Internationalfixedincomesecuritiesmakeupasignificantportionoftheglobalinvestablemarket.Whileinvestorsininternationalbondsareexposed totheriskofinterestratemovements,thepoliticallandscape,andtheeconomiesofmanydifferentmarkets,we’veshownthattheprimaryfactorsdrivinginternationalbondpricesarerelativelyuncorrelatedtothesameU.S.factors,whichimpliesadiversificationbenefit.Ofcourse,investorsarealsoexposedtocurrencymovements,whichhaveanimportantroleindeterminingtheriskofinternationalbonds.We’veshownthatonaverage,thevolatilityofcurrenciescanoverwhelmanydiversificationbenefitthatinternationalbondsmaybringtoa

diversifiedportfolio.Ontheotherhand,withthatcurrencyriskhedged,anallocationtointernationalbondscanleadtoloweraverageportfoliovolatilityovertime.

Tomakethestrategicdecisiontoincludeinternationalbondsinadiversifiedportfolio,aninvestorshouldweighthetrade-offsamongseveralfactors:thepotentialtoreduceportfoliovolatility,exposuretothelargestglobalassetclass,thecostsofimplementation,andtheinvestor’sownviews onthefuturepathoftheU.S.dollar.Basedonourfindings,webelievethatmostinvestorsshouldconsideraddinghedgedforeignbondstotheirexistingdiversifiedportfolios.

Figure 11.

Hedging costs: Annualized bid-ask spread for 1-month forward relative to U.S. dollar

The cost of hedging currency risk has declined over time

0

0.1

0.2

0.3

0.4

0.5

0.6%

Bid

-ask

spr

ead

Notes: We used the annualized bid-ask spread on a 1-month currency forward contract as a proxy for the cost of implementing a constant rolling hedge for each individual currency. In practice, 3- or 6-month forwards may be used. The weighted average hedging cost is approximated by combining the currency forwards according to the historical market weight of the outstanding debt of each entity. All data through December 31, 2013.

Sources: Vanguard, Thomson Reuters Datastream, and Barclays.

Australian dollarCanadian dollarEuroSwiss franc

YenBritish poundWeighted average hedging cost

Swedish krona

2013201220112010200920082007200620052004200320022001200019991998199719961995199419931992

18

Appendix. The Vanguard Capital Markets Model

TheVanguardCapitalMarketsModel(VCMM) isaproprietaryfinancialsimulationtooldevelopedandmaintainedbyVanguard’sInvestmentStrategyGroup.TheVCMMforecastsdistributionsoffuturereturnsforawidearrayofbroadassetclasses.TheseincludeU.S.andinternationalequitymarkets,severalmaturitiesoftheU.S.Treasuryandcorporatefixedincomemarkets,internationalfixedincomemarkets,U.S.moneymarkets,commoditiesmarkets,andcertainalternativeinvestmentstrategies.Theresultsshowninthispaperaredrawnfrom10,000VCMMsimulationsbasedonmarketdataandotherinformationavailableasofDecember31,2013.

TheVCMMisgroundedintheempiricalview thatthereturnsofvariousassetclassesreflect thecompensationinvestorsreceiveforbearingdifferenttypesofsystematicrisk(orbeta).Using alongspanofhistoricalmonthlydata,theVCMMestimatesadynamicstatisticalrelationshipamongglobalriskfactorsandassetreturns.Basedonthesecalculations,themodelusesregression-basedMonteCarlosimulationmethodstoproject

relationshipsinthefuture.Byexplicitlyaccountingforimportantinitialmarketconditionswhengeneratingitsreturndistributions,theVCMMframeworkdepartsfundamentallyfrommore basicMonteCarlosimulationtechniquesfoundincertainfinancialsoftware.Thereaderisdirected totheresearchpaperVanguard Capital Markets Model(Wallick,Aliaga-Díaz,andDavis,2009)forfurtherdetails.

TheprimaryvalueoftheVCMMisinitsapplicationtoanalyzingpotentialclientportfolios.VCMMasset-classforecasts---comprisingdistributionsofexpectedreturns,volatilities,andcorrelations---arekeytotheevaluationofpotentialdownsiderisks,variousrisk-returntrade-offs,anddiversificationbenefitsofvariousassetclasses.Althoughcentraltendenciesaregeneratedinanyreturndistribution,Vanguardstressesthatfocusingonthefullrangeofpotentialoutcomesfortheassetsconsidered,suchasthedatapresentedinthispaper,isthemosteffectivewaytouseVCMMoutput.

19

References

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LaBarge,KarinPeterson,2010.Currency Management: Considerations for the Equity Hedging Decision.ValleyForge,Pa.:TheVanguardGroup.

Lemco,Jonathan,RogerAliaga-Díaz,andCharles J.Thomas,2010.What’s Next for the Eurozone? ValleyForge,Pa.:TheVanguardGroup.

Mark,NelsonC.,1995.ExchangeRatesandFundamentals:EvidenceonLong-HorizonPredictability.American Economic Review85(1):201–18.

Meese,RichardA.,andKennethS.Rogoff,1983.EmpiricalExchangeRateModelsoftheSeventies:DoTheyFitOutofSample?Journal of International Economics14:3–24.

Meredith,Guy,andMenzieD.Chinn,1998.Long-Horizon Uncovered Interest Rate Parity.NBERWorkingPaper6797.Cambridge,Mass.:NationalBureauofEconomicResearch.

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Philips,ChristopherB.,2014.Global Equities: Balancing Home Bias and Diversification.ValleyForge,Pa.:TheVanguardGroup.

Philips,ChristopherB.,FrancisM.KinniryJr., DavidJ.Walker,andCharlesJ.Thomas,2011. A Review of Alternative Approaches to Equity Indexing.ValleyForge,Pa.:TheVanguardGroup.

Philips,ChristopherB.,JoanneYoon,MichaelA.DiJoseph,RaviG.Tolani,ScottJ.Donaldson,andToddSchlanger,2013.Emerging Market Bonds: Beyond the Headlines.ValleyForge,Pa.: TheVanguardGroup.

Solnik,Bruno,1974.AnEquilibriumModeloftheInternationalCapitalMarket.Journal of Economic Theory8(4):500–524.

Stockton,KimberlyA.,ScottJ.Donaldson,andAnatolyShtekhman,2008.Liability-Driven Investing: A Tool for Managing Pension Plan Funding Volatility. ValleyForge,Pa.:TheVanguardGroup.

Thomas,CharlesJ.,andDonaldG.Bennyhoff,2012.A Review of Alternative Approaches to Fixed Income Indexing.ValleyForge,Pa.:TheVanguardGroup.

Wallick,DanielW.,RogerAliaga-Díaz,and JosephDavis,2009.Vanguard Capital Markets Model.ValleyForge,Pa.:TheVanguardGroup.

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